To solve this problem, it's essential to understand whether the problem requires the calculation of permutations or combinations. Here, we need to determine how many ways we can choose a starting five from a team of twelve members.
### Key Concepts:
1. Permutations: Used when the order of selection matters.
2. Combinations: Used when the order of selection does not matter.
In the context of picking a starting five for a basketball team, the order in which the players are picked does not matter; we are only interested in which players are chosen.
Therefore, we need to use combinations to solve this problem. The formula for combinations is given by:
[tex]\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \][/tex]
where:
- [tex]\( n \)[/tex] is the total number of items.
- [tex]\( r \)[/tex] is the number of items to choose.
- [tex]\( ! \)[/tex] denotes factorial, which is the product of all positive integers up to that number.
In this specific problem:
- [tex]\( n = 12 \)[/tex]: Total number of players.
- [tex]\( r = 5 \)[/tex]: Number of players to choose for the starting five.
Using the combination formula, we have:
[tex]\[ \binom{12}{5} = \frac{12!}{5!(12-5)!} \][/tex]
After calculating this formula, we find:
[tex]\[ \binom{12}{5} = 792 \][/tex]
Therefore, the number of ways to pick a starting five from a basketball team of twelve members is 792.
Hence, the best answer from the choices provided is:
b. Combination; [tex]\(\binom{12}{5} = 792\)[/tex]
And the correct selection is:
B
